There technically is a cycloid in SFEX3, but it's unplayable and in fact is never even played against without a cheat device. Its moveset hardly has any hitboxes, either. It's really nothing more than a solid mesh that was still given the Cycloid name for whatever reason.
As for that portrait, I don't think it ever appears in-game with a green color. Its silhouette acts as a placeholder in the character select screen.
It seems that the only cycloids that were ever meant to see the light of day were Cycloid Beta and Cycloid Gamma. Goddamn, though. Two feels like a million.
Maybe they'll pad out the EX profiles with these characters (they're referred to as Zako A, B, and C, supposedly. And this is not necessarily in order since I don't know or care which is which):
All unplayable, still given the "Cycloid" name for some reason. You just kill these things during the end credits, hearing the excessive screaming in the process. It's like a fever dream.
Sorry to flood this thread with walls of images about some bizarre-ass, slightly obscure game.